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C5×D13×D99 #38787883

order25740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D13×D99
unambiguous semidirect product(C9×D13)⋊(C5×D11)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C22
derived, HallC9×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ C2×D9
HallC5×C9×C13 ⋊ C2×D11
HallC5×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D9
HallC9×C13 ⋊ C2×C5×D11
HallC9×C11 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D99
HallC5×C11 ⋊ D9×D13
HallC5×C9 ⋊ D11×D13
SylowC13 ⋊ C2×C5×D99
SylowC11 ⋊ C5×D9×D13
SylowC9 ⋊ C5×D11×D13

Subgroups

subgroupG/H
center, hypercenterC5D13×D99
commutator, cosocle, hypocenterC9×C11×C13C22×C5
FrattiniC3C5×D13×D33
FittingC5×C9×C11×C13C22
socleC3×C5×C11×C13C2×D3
LCSG ▷ C9×C11×C13
UCSC1 ◁ C5

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 6435

A minimal faithful permutation representation — 2 generators on 38 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,15)(14,18)(16,17)(19,20)(21,22,24,26,28,30,32,33,31,29,27,25,23)(34,35,36,37,38);(1,2,4,6,8,10,11,9,7,5,3)(12,17,19,18,13,15,14,20,16)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 114);